Yuan-Hong Ren

When Do Restricted Sumsets Cover a Finite Abelian Group?

For a subset $A$ of a finite abelian group $G$, let $\Sigma_k(A)$ denote the set of sums of $k$ distinct elements of $A$, and let $\Sigma(A)=\bigcup_{k\ge1}\Sigma_k(A)$. The problem of determining when $\Sigma(A)=G$ goes back to Erd\H{o}s and Heilbronn. Nguyen and Vu later formulated the corresponding fixed-length ques...